Abstract

The application of SSM/I multi-parameter satellite retrievals in operational
weather analysis and forecasting is addressed. More accurate multi-parameter
satellite retrievals are now available from the SSM/I neural network algorithm
which also provide greater coverage, than some of the initial algorithms.
These retrievals (ocean surface wind speed, columnar water vapor and columnar
liquid water), when analyzed together, can be interpreted to provide an
internally consistent description of synoptic weather patterns over the
oceans. Three SSM/I sensors which are currently in orbit provide sufficient
amount of data to be successfully used in real-time operational environment.
Several examples are presented to illustrate that significant meteorological
features such as fronts, convective areas and areas with high probability
of precipitation can be identified and observed in the SSM/I fields retrieved
by the new algorithm from the data composed from three SSM/I sensors. The
most recent version of neural network algorithm retrieves simultaneously
four geophysical parameters: ocean surface wind speed, columnar water vapor,
columnar liquid water, and sea surface temperature. It is the multi-parameter
simultaneous retrieval that is unique about the new algorithm, allowing
the information from one variable to contribute to the improvement of the
other variables (e.g., improved accuracy of wind speed retrievals at high
wind speed). Further, the neural network wind speed data were able to show
a positive impact on the Data Assimilation System at NCEP, and these data
were recently incorporated as a part of operational data assimilation system.

1. Introduction.

Beginning in 1987, a series of Special Sensor Microwave/Imager (SSM/I)
instruments have been launched through the Defense Meteorological Satellite
Program (DMSP) (Hollinger et al. 1987).
DMSP SSM/I satellites are polar orbiting satellites with a 102 minute orbit.
Each satellite provides coverage over a particular ocean basin twice a
day, once during a descending orbit and once during an ascending orbit.
The SSM/I generates brightness temperatures in seven channels at four frequencies
(19, 22, 37, and 85 GHz), each with vertical and horizontal polarization
(22 GHz channel senses only vertical polarization). The spatial resolution
is about 50km at 19 and 22 GHz, about 30 km at 37 GHz and 15km at 85 GHz.
The SSM/I infers brightness temperatures from the ocean surface passively,
receiving microwave radiation emitted by the ocean surface and passed through
the atmosphere. The emission is effected by the surface wind speed (which
changes the roughness of the ocean surface) and by the sea surface temperature
(SST). The propagation of the microwave radiation through the atmosphere
is influenced by the integrated amounts of water vapor and liquid water
in the atmospheric column (Wentz 1992, 1997). As a result the brightness
temperatures carry signals from all these geophysical parameters and can
then be converted into geophysical parameters (surface wind speed, columnar
water vapor, columnar liquid water, and SST) using retrieval algorithms.

DMSP satellites have substantially increased the amount of real-time
meteorological data that is acquired over the oceans, which are used subjectively
by marine meteorologists to improve ocean surface weather map analyses,
and objectively by numerical analysis systems to provide initial conditions
for numerical weather prediction models. With three satellites in orbit
(F11, F13 and F14) and with a swath width of about 1400 km for each of
the satellites, high-resolution coverage is now available almost globally
on a daily basis.

Empirical retrieval algorithms (or transfer functions) have been developed
separately for various geophysical parameters such as surface wind speed
(Goodberlet et al. 1989; Petty 1993) (see also Appendix A), columnar water
vapor (Alishouse et al. 1990) and columnar liquid water (Weng and Grody
1994). The empirical retrieval algorithm is usually derived from a high-quality
data set that collocates the satellite brightness temperatures with buoy-
and/or radiosonde-measured geophysical variables in time and space. The
physically based algorithms use a large amount of such empirical data for
parametrizations (Wentz 1997). The collocated matchup data set requires
a large data sample in order to represent a wide range of global meteorological
events. High wind speed events have been fairly rare in most matchup data
sets because winds speeds of gale force (> 17 m/s) or greater at a given
time cover no more than 5 % of the global ocean surface.

Some of the initially developed retrieval algorithms are based on a
simple statistical technique such as linear regression and, as a result,
have limited retrieval capabilities. Careful validations and evaluations
of the retrievals over a period of time are required to sample a wide range
of meteorological conditions and to determine the conditions for which
the transfer functions do not perform well. Such validations invariably
show that the initial algorithms have serious limitations in providing
good quality data over regions where weather conditions are rapidly changing.
Hence the necessity to examine the possibility of making improvements to
the retrieval algorithm arises (Gemmill et al. 1996).

The purpose of this paper is to address the application of improved
SSM/I multi-parameter satellite retrievals that are now available at NCEP
due to using the latest SSM/I neural network algorithm and data from three
SSM/I sensors in operational weather analysis and forecasting. This algorithm
provides detailed and accurate fields of meteorological variables over
the oceans and the coverage is extensive because of the number of satellites
that are currently in operation. These fields can be seen at:http://polar.ncep.noaa.gov/marine.meteorology/marine.winds/.
The new neural network algorithm derives surface wind speed (W),
columnar water vapor (V), columnar liquid water (L) and sea
surface temperature (SST) simultaneously from SSM/I brightness temperatures.
Although these parameters have already been retrieved separately by other
techniques, it is the simultaneous retrieval by the neural networks (NNs)
that is unique, allowing the information from one parameter to contribute
to a better estimate of the other parameters. The parameters retrieved
by the NN, when analyzed together, can provide
information about synoptic weather patterns over the oceans (Gemmill and
Krasnopolsky 1998) that is more comprehensive and internally consistent
than that from a single parameter (see also Appendix A).

In Section 2 we briefly review recent works on improvement of SSM/I
retrievals. In Section 3 we discuss possible approaches to interpreting
the data fields derived from SSM/I and presents several examples which
show that significant meteorological features like fronts, convective areas
and areas with high probability of precipitation can be identified and
observed in SSM/I fields retrieved by the new algorithm. In Appendix A
we review prior works on SSM/I algorithm development. In Appendix B some
background NN theory which is relevant for SSM/I algorithm development
is introduced.

2. Work on Improvement of Accuracy of SSM/I Retrievals

A retrieval algorithm relates a vector of geophysical parameters, g,
which in our case is g = {W, V, L, SST } to the vector
of satellite measurements, T, which in our case is a vector
of SSM/I brightness temperatures. This relationship can be symbolically
represented as

g = f (T)
(1)

where f is usually called a transfer function. In the
case of SSM/I the transfer function f is essentially nonlinear
especially when the amount of moisture in the atmosphere is significant
(Petty 1993, Stogryn et al. 1994). Each particular retrieval algorithm
corresponds to a particular choice of geophysical parameters to retrieve
(vector g), brightness temperatures to use (vector T),
a mathematical (statistical) model for the transfer function f (see
Appendix A for details), and a development data set.

Most previous SSM/I retrieval algorithms (Appendix A) retrieve one variable
at a time. The original global algorithm for retrieving ocean surface wind
speed from SSM/I was developed by Goodberlet et al. (1989) (GSW algorithm).
This algorithm is based on linear regression and is primarily limited to
low moisture conditions. Further, there were only a few wind speed observations
in the high range (>18 m/s) available in the matchup data set used in the
formulation of the algorithm, so the GSW algorithm could not be expected
to perform well at retrieving high winds. Because of these limitations,
wind speeds cannot be accurately determined with this algorithm in areas
with significant levels of atmospheric moisture (e.g., in large parts of
the tropics) and cannot be retrieved in the vicinity of storms and fronts.
Petty (1993) introduced a nonlinear correction to the GSW algorithm (GSWP
algorithm) which improves the accuracy of the wind speed retrievals in
areas with higher amounts of the water vapor (in much of the tropics for
example). Recently (October 1997) this version of the algorithm became
operational via the shared data processing center at Fleet Numerical Meteorological
and Oceanographic Center.

Several algorithms have been developed to retrieve columnar water vapor
(Alishouse et al. 1990; Petty 1993) and columnar liquid water (Weng and
Grody 1994; Weng et al. 1997). However, all these algorithms (including
wind speed algorithms) have been developed independently using different
data sets. They were formulated without taking into account co-dependency
of these parameters and without accounting for the physical relationships
among the parameters.

For the past five years, NCEP has concentrated on improving the accuracy
of SSM/I satellite derived ocean surface wind speeds, columnar water vapor,
and columnar liquid water for both marine meteorology applications and
numerical weather prediction (NWP). A series of algorithms (see Fig. 1)
has been formulated using neural networks (NNs), each one more complex
and accurate than the previous one. A brief review of NN theory as related
to our topic is presented in Appendix B. NNs were chosen because they have
been highly successful in meteorological and oceanographic applications
(Hsieh and Tang 1998) and in resolving complex non-linear relationships
between the sensor output and the atmospheric variable of interest (Thiria
et al. 1993, Stogryn et al. 1994, Jung et al. 1998). Hence, they were able
to provide an effective method for dealing with high moisture conditions
while deriving wind speeds. In 1994 , an initial NN algorithm (OMBNN1)
was formulated (Krasnopolsky et al. 1995a), using the same matchup data
base of SSM/I brightness temperatures (from the F8 satellite) with buoy
wind speeds that was used to develop the GSW algorithm. The OMBNN1 algorithm
used brightness temperature from four of the SSM/I channels to produce
one output, wind speed. That initial study showed that OMBNN1 was capable
of providing ocean surface wind speeds from SSM/I brightness temperatures
with better accuracy, and in areas with higher levels of atmospheric moisture,
than the GSW algorithm. But when the OMBNN1 algorithm was applied to global
SSM/I data for operational use, the algorithm was unable to provide high
wind speeds ( > 15 m/s) with acceptable accuracy. Many wind speed retrieval
algorithms have problems with retrieving high wind speeds (Boutin and Etcheto
1996). This problem is usually attributed to the lack of high winds in
the matchup data.

In order to improve accuracy in the high wind speed range, a new neural
network, OMBNN2 (Krasnopolsky et al. 1995b), was developed by emphasizing
the few high winds that were in the original data set, and including a
bias correction. Also, the OMBNN2 algorithm used brightness temperatures
from five of the SSM/I channels to produce one output, wind speed. The
OMBNN2 algorithm did improve the ocean surface wind speeds compared to
OMBNN1, but still could not produce higher wind speeds with the desired
accuracy. Also, the OMBNN2 algorithm incorporates a bias correction which
is sensor dependent. Nevertheless, wind speed fields produced by OMBNN2
were able to show high-resolution structure of the wind speed patterns
over the ocean normally not observed in conventional surface data sets.
The output from the OMBNN2 algorithm has been evaluated within the NCEP
global prediction model (Yu et al. 1997) to determine its impact. The evaluation
showed that the wind speed analyses and forecasts based on the OMBNN2 neural
network ocean surface wind speed data were better than those based on the
GSW algorithm when compared to buoy data.

More recently, a rather comprehensive SSM/I and buoy matchup data set
was provided by the Naval Research Laboratory (NRL) for algorithm development.
The NRL data set contains more data and has better coverage of high wind
events than the previous data set used by GSW. Further, other high latitude
SSM/I ocean weather ship matchup data sets were obtained from Bristol University
(D Kilham, personal communication). The NN was retrained with the new wind
speed data for one parameter (wind speed only) retrievals, but large errors
at high wind speeds still occurred.

Hence, a new NN architecture was formulated (Fig. 1) which takes into
account the interdependence of physically-related atmospheric and oceanic
parameters (wind speed, columnar water vapor, columnar liquid water and
sea surface temperature). The new OMBNN3 algorithm (Krasnopolsky et al.
1998a,b, 1997, 1996) utilizes five SSM/I brightness temperature channels.
It simultaneously produces all four parameters. This algorithm was trained
to preserve proper physical relationships among these parameters. The algorithm
has extended the range of wind speeds over which useful retrievals can
be obtained. It not only improves the accuracy of the wind speed retrievals,
especially at high wind speeds (without bias correction), but makes available
three additional fields. Table 1 indicates the importance of the inclusion
of water vapor, liquid water, and SST in retrieval algorithms on the accuracy
of wind speed. The GSW is the original linear algorithm, and the GSWP algorithm
contains the water vapor correction suggested by Petty (1993). The RMS
error statistics of the OMBNN3 algorithm, which takes into account also
the liquid water and SST influences, are lower than those of the GSWP algorithm
over all wind speeds, and especially at wind speeds > 15 m/s.

Table 1. Comparison of bias, algorithm RMS error (sensor noise
and matchup uncertainties are removed), total RMS error and high wind speed
(W>15m/s) RMS error, for buoy wind speed vs. SSM/I wind speed, and for
five SSM/I wind speed algorithms, with all errors in m/s. Errors calculated
over more than 15,000 buoy/SSM/I matchups. Numbers outside the parentheses
correspond to clear and in the parentheses to clear+cloudy conditions.

Figure 1. Evolution
of the SSM/I Neural Network architecture from OMBNN1 to OMBNN3. Brightness
temperature from SSM/I channels used as input to the algorithms and geophysical
parameters retrieved as outputs from the algorithms are shown. OMBNN1 has
four inputs, one hidden layer with two neurons and one output: wind speed.
OMBNN2 has five inputs, one hidden layer with two neurons and one output:
wind speed. OMBNN3 has five inputs, one hidden layer with 12 neurons and
four outputs: wind speed, columnar water vapor, columnar liquid water,
sea surface temperature.

Fig. 2 shows the wind speed difference (buoy minus satellite wind speeds)
characteristics (retrieval errors in wind speed) as functions of three
other parameters: columnar water vapor, columnar liquid water and sea surface
temperature for three algorithms GSW, GSWP and OMBNN3. Including nonlinear
water vapor correction in GSWP reduced the bias and its dependence on the
water vapor concentration (and partly on SST which is closely related to
water vapor); however, it did not reduce its dependence on the liquid water
concentration. This correction also did not significantly improve the standard
deviation of the differences. The OMBNN3 algorithm, with its simultaneous
multi-parameter retrievals, reduced the bias and its dependence on all
three other parameters together with a significant improving the standard
deviation of the differences.

NN retrievals for columnar water vapor and columnar liquid water are
in good agreement with existing SSM/I algorithms. No attempt was made to
verify these retrievals against observed data because of the lack of collocated
observations. The details of the development of OMBNN3 and its validation
have been documented by Krasnopolsky et al. (1998a,b, 1997, 1996). The
accuracy of the SST retrievals is lower than the accuracy of high resolution
AVHRR SST; however, the retrieved SSTs give secondary information that
improves the accuracy of the wind speed retrievals, especially at high
wind speeds. Because this algorithm is inherently nonlinear, it increases
areal coverage in areas with significant levels of atmospheric moisture
and under more active and critical weather systems such as storms and fronts.

Comparison studies of the impact of ocean surface wind retrievals on
the Global Data Assimilation System (GDAS) at NCEP showed a more positive
impact using retrievals from OMBNN2 algorithm than from the GSW algorithm
(Yu et al. 1997). In the meanwhile, the OMBNN3 algorithm was developed,
and the wind speed retrievals from the OMBNN3 algorithm were shown to be
better than retrievals from the OMBNN2 algorithm, especially for high winds.
Impact studies similar to those performed for OMBNN2 have been performed
using the OMBNN3 algorithm and further positive impact was observed as
compared to both GSW and OMBNN2 (Yu 1998). Based on these results the OMBNN3
ocean surface wind speed retrievals were incorporated into the operational
GDAS at NCEP in April 1998.

In this section, we show that the three meteorological variables (ocean
surface wind speed, columnar water vapor and columnar liquid water) which
are produced simultaneously by the new OMBNN3 algorithm can provide a clear
descriptive analysis of the weather over the ocean. Moreover, we show how
the interpretation of the three variables together can give a more complete
description of marine weather than by using the ocean wind speed data alone.

The ocean surface wind speed data have the most direct use in marine
weather analysis and weather forecasting. Although these data provide wind
speed only, the extensive coverage of the three satellites depicts high-resolution
wind speed patterns across synoptic weather systems. These data can be
used directly to improve ocean surface wind analyses, and indirectly to
improve sea level pressure analyses.

The columnar water vapor and columnar liquid water are the vertically
integrated values through the entire atmosphere. The columnar water vapor
is also known as "total precipitable water", which is the depth of water
that would fall on the ocean if all the water vapor were condensed and
precipitated. Columnar water vapor is an air mass characteristic closely
related to synoptic scale features. Its primary source is the warmer waters
of the tropics, and it is advected to higher latitudes by storms and low-
and mid-level jet streams. As a result, regions with large gradients of
columnar water vapor have been shown to be good objective indicators of
the position of an ocean surface front (Katsaros et al. 1989) .

The liquid water resides in clouds, and is more directly related to
regions of precipitation and to active weather systems such as storms and
fronts (McMurdie and Katsaros, 1996). Large liquid water amounts are generally
associated with strong convective activity (cumulus clouds) and turbulent
surface weather conditions, whereas small amounts of liquid water are associated
with near neutral or stable regions (stratiform clouds) and constant or
steady surface weather conditions.

OMBNN3 has been extensively evaluated at
NCEP using real-time data from F10, F11, F13 and F14 SSM/I instruments.
Simultaneous retrievals of wind speed, columnar water vapor and columnar
liquid water fields using OMBNN3 were examined to reveal significant information
concerning weather patterns over the ocean. Two examples of such a consideration
are presented below.

a. Some Examples

Here we present two examples to show the use of the satellite derived data
retrieved from the OMBNN3 algorithm. The examples cover two regions: one
for the eastern North Pacific, and one for the western North Atlantic Oceans.
For each case, a marine weather map analysis is first presented to identify
major weather features over the region (Figs 3 and 5). Marine weather maps
for the North Pacific Ocean and the North Atlantic Ocean are produced every
six hours by the Marine Prediction Center. These analyses combine a variety
of data sources, including the six hour sea level pressure forecast from
the global numerical weather prediction model as a first guess, AVHRR satellite
cloud imagery, and quality controlled surface data from ships, fixed and
drifting buoys and coastal stations.

data from buoys and ship, (e) ERS2 scatterometer wind vector data(3),
and (f) the sea level pressure analysis available from the NCEP Global
Data Analysis System. The plots of satellite data are within a +/- 3 hour
time window about the analysis time. The SSM/I data are a composite from
three DMSP satellites (F11, F13 and F14), which together provide almost
complete and extensive regional coverage. The two cases represent synoptic
weather patterns that were well analyzed from other real-time data sources,
so there are no discrepancies between the data sets in terms of the meteorology.
Their purpose is to show that the variables retrieved from the SSM/I through
the NN algorithm provided information consistent with the actual weather
situation. These examples demonstrate that neural networks have the capability
to retrieve useful meteorological information from SSM/I brightness temperatures.

1)EXAMPLE 1.
EASTERN NORTH PACIFIC
OCEAN,
12MARCH
1998,
06UTC.

The marine weather analysis for the northeastern Pacific on 12 March 1998,
06UTC is presented in Fig. 3. The main weather feature in the northeast
Pacific is a moderate storm with a central pressure of 982 mb, located
near 43 N and 138 W, 600 nm west of the Oregon coast. The storm itself
is labeled a GALE, indicating winds above 33 knots(4).
Within its circulation, this storm has wrapped around the occlusion from
the north to the northwest of the center, with a cold front to the east,
located about 300 nm from the Washington to California coasts near 131
W. The front trails back toward the west, and eventually toward the northwest
to the leading edge of the next storm which is in the central Pacific near
the date line. There is another small low just off the southern coast of
Alaska. A major high pressure ridge lies across the southern part of the
region along 26-28 N. Winds are near 30 knots to the southwest of the storm,
and about 40 knots closer to the storm center.

The sea level pressure analysis from the global model at 06 UTC shows
little difference from the MPC analysis. The MPC analysis has the storm
slightly deeper by 4 mb than the global model analysis (Fig. 4f).

The SSM/I wind field (Fig. 4a) shows the storm to be fairly circular
and moderate in size. The yellow region shows the outer limit of the 20
knot winds, and the orange region shows the gale force region southwest
of the center and 40 knot winds near the center. Due to high moisture content
that makes retrievals impossible, and due to an occasional bad scan line,
there are areas without wind speed data. The northward moving occluded
front is associated with a band of high wind speeds (30 knots). Just ahead
of the eastward moving cold front there is a wind band with winds up to
25-30 knots, but the strongest winds are masked due to high moisture contamination
(possible rain). The weak low south of Alaska has winds near 30 knots along
the coast. The storm further west is already generating 40-45 knot winds
ahead of the occlusion.

The liquid water (Fig. 4b) shows a wrap-around pattern along the cold
front and then along the occlusion into the center. The greatest liquid
water values quite likely are associated with rain areas precede the occlusion
and cold front. Drier air is indicated behind the fronts. The water vapor
(Fig. 4c) shows the distinct pattern associated with the air masses. The
large water vapor gradient zone recognized as a quantitative parameter
for the location of oceanic fronts by Katsoras et al. (1989) clearly depicts
the location of the cold front. The water vapor shows a strong flow of
moist air moving from north of Hawaii to the U.S. northwest coast.

The in-situ buoy and ship wind data (Fig. 4d) are plotted four times
a day at the standard synoptic times of 00, 06, 12 and 18 UTC. The satellite
data are taken within three hours of the surface ship and buoy data. Although
the winds show the circulation associated with a storm, the intensity and
location of the storm center can be not determined from the ship and buoy
data alone. Determination of those values is aided by the SSM/I derived
data, and where there are in-situ surface wind reports, they corroborate
the values of the SSM/I derived wind speed data. Likewise, the ERS2 scatterometer
wind data (Fig. 4e) and SSM/I wind data are in close agreement.

2) EXAMPLE 2. WESTERN NORTH
ATLANTIC OCEAN, 25 FEBRUARY
1998, 12UTC

The main weather feature in the western North Atlantic is a moderate storm
with a central pressure of 984 mb, located near 42 N and 68 W, 600 nm off
the coast of New England (Fig. 5). That storm is labeled STORM, indicating
wind speeds above 48 knots. An occlusion extends from the north to the
southeast, with a cold front far out in the Atlantic trailing back to Jamaica.
There is another major storm off Greenland, and a minor storm in the central
Atlantic near 30N. A major high pressure ridge is oriented north-south,
centered at 48 N and 42 W (1037 mb). The plotted winds show a rather large
region of strong winds (35-45 knots) within 600-800 nm of the center of
the storm. The sea level pressure analysis from the numerical global model
at 12 UTC (Fig. 6f) shows little difference from the manual MPC analysis
(Fig. 5).

The SSM/I wind field (Fig. 6a) shows the storm to be fairly circular.
The yellow region shows the outer limit of the 20 knot winds, and the orange
region shows the gale force winds around the center of the system with
speeds to 45 knots. The SSM/I data indicate 50 knots winds for the Greenland
storm. SSM/I data also indicate a band of 35 knot winds on the western
side of the weak system in the central Atlantic.

The liquid water values (Fig. 6b) are greatest to the southwest of the
storm center, east of Cape Hatteras and south of Cape Cod, associated with
a trough line crossing the area east of the Gulf Stream.

The water vapor (Fig. 6c) shows the distinct air mass pattern, but does
not identify the storm system very well. However, the associated fronts
are clearly identified, especially by the large water vapor gradient across
the southwest portion of the figure. The water vapor shows a strong flow
of moist air moving from the Caribbean north into the eastern portion of
the storm.

The surface wind data reports (Fig. 6d) and the corresponding satellite
wind data are in close agreement. Note the region near 42 N between 50
W - 60 W, where the surface wind speed data approach 50 knots. The satellite
wind speeds in that region are only slightly lower, about 45 knots. Also,
note the ship report of 60 knots east of Greenland. In that area the satellite
data indicate wind speeds of 50 knots. Likewise, the ERS2 scatterometer
winds (Fig. 6e) and SSM/I winds are in close agreement. The wind speeds
and pattern are similar.

4. Summary

We have illustrated the analysis of meteorological variables retrieved
over the oceans from the SSM/I by the new neural network algorithm. In
its latest form, the multi-parameter neural network algorithm (OMBNN3)
has been shown to adequately provide weather information on ocean surface
wind speed data, columnar water vapor and columnar liquid water over a
wide range of values of these parameters.

The OMBNN3 algorithm retrieves wind speed, columnar water vapor, and
columnar liquid water signals contained in the SSM/I brightness temperatures,
with accuracies which are operationally useful. Also, multi-parameter retrievals
preserve the correct physical relationships among the retrieved parameters.

The algorithm generates high wind speeds (>15 m/s) in areas where such
winds are well supported by other data and are expected from sea level
pressure analyses.

The algorithm generates columnar water vapor patterns which are able
to delineate and characterize air masses. Low values are associated with
air masses originating in high latitudes that are cold and dry. High values
are associated with air originating in tropical areas that are warm and
moist. High gradients of the columnar water vapor are related to the position
of ocean surface fronts.

The algorithm generates columnar liquid water patterns which are related
to regions of water vapor convergence, resulting in clouds, which are closely
associated with cyclones and active frontal location.

Acknowledgments

We thank D.B. Rao for his thorough and critical review of this paper; Joe
Sienkiewicz, senior marine meteorologist, of the Marine Prediction Center
for his comments as a potential user of the SSM/I variables presented in
this paper and Laurence Breaker for his suggestions to improve the manuscript.
Also, we want to thank those who provided us with expanded collocated SSM/I
- buoy data sets; Gene Poe of the Naval Research Laboratory for providing
a preliminary raw version of the new NRL matchup database, David Kilham
of Bristol University for providing us with additional matchup data for
high latitudes, and Michael McPhaden and Linda Magnum for providing information
concerning TOGA-TAO buoys. Without this comprehensive data set, our results
could not have been extended through high wind speeds.

APPENDIX A

Brief review of prior empirical SSM/I retrieval
algorithms

The first global empirical wind speed retrieval
algorithm based on a multiple linear regression was developed by Goodberlet
et al. (1989). It is designated here as GSW. It uses a simple linear combination
of four SSM/I BTs to approximate the transfer function (TF), f,
(1) :

The GS algorithm developed by Goodberlet
and Swift (1992) attempts to improve the performance of the GSW algorithm,
using nonlinear regression with a nonlinear approximation of function f
of the following form:

(A2)

where WGSW is given by
(A.1). Since the nature of the nonlinearity of the SSM/I TF is not known
precisely, application of this nonlinear regression may not improve the
results. Because (A.2) has a singularity at = 1 or equivalently at |T37V
- T37H| = 30.7 K, when BTs fall close to this pole, this algorithm
generates spurious high wind speeds. The authors do not recommend using
this algorithm when |T37V - T37H| < 40. K (Goodberlet and Swift
1992); however, this limitation is not based on physical principles, but
rather it is caused by an improper choice of nonlinear regression function.

The nonlinear approximation introduced
by Petty (1993) is another type of regression algorithm. Nonlinear functions
introduced in the linear regression in this case represent the nonlinear
behavior of the transfer function (1) much better:

(A.3)

Here again, WGSW is given
by (A.1), -2.13 is a bias correction, and 0.2198V - 0.4008×10-2V2
is a nonlinear function which corrects the one-parameter linear TF (A.1)
for water vapor.

Single-parameter NN algorithms have been
introduced as an alternative to nonlinear regression (e.g., A.2) because
they can model the nonlinear behavior of TFs without specifying a particular
type of nonlinearity a priori. The NN algorithms developed by Stogryn et
al. (1994) and Krasnopolsky et al. (1995a) (OMBNN1) have identical architectures
which are shown in Fig. 1. The OMBNN1 algorithm is represented by expression
(B.3, Appendix B) where n = 4 (inputs - T19V, T22V, T37V, T37H),
m
=1
(output - W) and k = 2 (hidden nodes). An improved for high
wind speeds single-parameter NN algorithm was developed by Krasnopolsky
et al. (1995b), the OMBNN2 algorithm, has an architecture shown in Fig.
1. A new method of NN training which enhances learning at high wind speeds
by using a weighting schema which is inversely proportional to the wind
speed probability distribution was used. The OMBNN2 algorithm is represented
by expression (B.3) where n = 5 (inputs - T19V, T22V, T37V, T37H,
T85V), m =1 (output - W) and k = 2 (hidden nodes).

Single-parameter algorithms discussed above
retrieve a single geophysical parameter gi (e.g., surface
wind speed), using SSM/I BTs, without regard to any information about other
geophysical parameters which are related to, or correlated with, gi.
In this case, the signatures (contributions to BT) of these related parameters,
if they are not properly taken into account, act as additional noise (pseudo
noise) in the BT signal. As a result, first, useful information about related
geophysical parameters contained in these signatures is lost, and second,
this pseudo noise causes additional errors in the parameter of primary
interest, gi (e.g., wind speed). If the data set used
for algorithm development spans the full dynamical range of observed wind
speeds, water vapor, etc., these additional errors will not contribute
to the bias, but only to the scatter. However, for high values of wind
speed, atmospheric moisture, etc., where the data are sparse, a single-parameter
algorithm will produce a significant bias (and a higher scatter) for the
estimated parameter gi (see Fig. 2). This error is the
primary source of error in wind speed retrievals at high wind speeds. This
type of error can be minimized using simultaneous multi-parameter retrievals.
A
multi-parameter NN algorithm OMBNN3 (Krasnopolsky et al. 1998a,b, 1997,
1996) has an architecture shown in Fig. 1
and retrieves simultaneously four geophysical parameters: wind speed, columnar
water vapor, columnar liquid water, and SST. Multi-parameter retrievals
performed by this algorithm reduces error in the wind speed which is due
to co-variability of related geophysical parameters (see Fig. 2). The
OMBNN3 algorithm is represented by expression (B.3, Appendix B) where n
=
5 (inputs - T19V, T19H, T22V, T37V, T37H), m =4 (outputs
- W, V, L, SST) and
k = 12 (hidden nodes).

APPENDIX B

Neural networks and retrieval algorithms

As it was shown in Section 2, a retrieval
algorithm (transfer function) is a relationship, f, (1) (usually
nonlinear) between two vectors: a vector of geophysical parameters, g,
and a vector of satellite measurements, T, g = f (T
). Such a relationship between two vectors is called continuous
mapping.

Neural networks (NNs) are well-suited for
a very broad class of continuous approximations and mappings. Neural networks
consist of layers of uniform processing elements, nodes, units, or neurons.
The neurons and layers are connected according to a specific architecture
or topology. Fig. B.1 shows a simple architecture which is sufficient for
any continuous nonlinear mapping, a multilayer perceptron. The number of
input neurons, n, in the input layer is equal to the dimension of
input vector X (T in our particular case).
The number of output neurons, m, in the output layer is equal to
the dimension of the output vector Y (g in
our particular case). A multilayer perceptron always has at least one hidden
layer with k neurons in it. A typical neuron (processing element)
usually has several inputs (components of vector X), one
output, zj, and consists of two parts, a linear part
and a nonlinear part. The linear part formes the inner product of the input
vector X with a weight vector j (which
is one column of the weight matrix ji ), and may also
add a bias term, Bj. This linear transformation of the
input vector X feeds into the nonlinear part of the neuron
as the argument of an activation function. For the activation function,
itis sufficient that it be a Tauber-Wiener (nonpolynomial,
continuous, bounded) function (Chen and Chen 1995a,b). Here we use a standard
activation function - the hyperbolic tangent. Then, the neuron output,
zj
, can be written as,

(B.1)

The neuron is a nonlinear element because
its output zj is a nonlinear function of its inputs X.

From the discussion above it is clear that
NN generally perform a continuous (and nonlinear) mapping of an input vector
Xn(n is the dimension of the input vector or the number of inputs)
onto an output vector Ym(m is the
dimension of the output vector or the number of outputs). Symbolically,
this mapping can be written as,

For the topology shown in Fig. B.1 for
a NN with k neurons in one hidden layer, and using (B.1) for each
neuron in the hidden and output layers, (B.2) can be written explicitly
as,

(B.3)

where the matrix ji and
the vector Bj represent weights and biases in the neurons
of the hidden layer; qj in Rk×m
and theqin Rmrepresent weights and
biases in the neurons of the output layer; and aq
and bq are scaling parameters. It can be seen
from (B.3) that any component (yq) of the NN's
output vector Y is a complicated nonlinear function of all
components of the NN's input vector X. It has been shown
(e.g., Chen and Chen 1995a,b, Funahashi 1989) that a NN with one hidden
layer (e.g., NN (B.3)), can approximate any continuous mapping defined
on compact sets in Rn.

For each particular problem, n and
m
are determined by the dimensions of the input and output vectors
X
and
Y. The number of hidden neurons, k, in each particular case
should be determined taking into account the complexity of the problem.
The more complicated the mapping, the more hidden neurons are required.
Unfortunately, there is no universal rule that applies. Usually
k
is determined by experience and experiment. In general, if k is
too large, the NN will reproduce noise as well as the desired signal. Conversely,
if k is too small, the NN is unable to reproduce the desired signal
accurately. After these topological parameters are defined, the weights
and biases can be found, using a procedure which is called NN training.
A number of methods have been developed for NN training (e.g., Beale and
Jackson 1990, Chen 1996). Here we use a simplified version of the steepest
(or gradient) descent method known as the back-propagation training algorithm.

Because the dimension of the output vector
Y
may obviously be greater than one, NNs are well suited for modeling multi-parameter
transfer functions (1). All components of the output vector Y
are produced from the same input vector
X. They are related
through common hidden neurons; however, each particular component of the
output vector Y is produced by a separate output neuron which
is unique.